% !TeX root = ./main.tex

% Adapted for use with ustcthesis.
% Original code is at https://github.com/goodfeli/dlbook_notation/blob/master/math_commands.tex

%%%%% NEW MATH DEFINITIONS %%%%%

\newcommand\ceil[1]{\lceil #1 \rceil}
\newcommand\floor[1]{\lfloor #1 \rfloor}


% Vectors
%\newcommand\Vector[1]{\symbf{#1}}

\newcommand\0{{\Vector{0}}}
\newcommand\vzero{{\Vector{0}}}
\newcommand\1{{\Vector{1}}}
\newcommand\vone{{\Vector{1}}}

\newcommand\va{{\Vector{a}}}
\newcommand\vb{{\Vector{b}}}
\newcommand\vc{{\Vector{c}}}
\newcommand\vd{{\Vector{d}}}
\newcommand\ve{{\Vector{e}}}
\newcommand\vf{{\Vector{f}}}
\newcommand\vg{{\Vector{g}}}
\newcommand\vh{{\Vector{h}}}
\newcommand\vi{{\Vector{i}}}
\newcommand\vj{{\Vector{j}}}
\newcommand\vk{{\Vector{k}}}
\newcommand\vl{{\Vector{l}}}
\newcommand\vm{{\Vector{m}}}
\newcommand\vn{{\Vector{n}}}
\newcommand\vo{{\Vector{o}}}
\newcommand\vp{{\Vector{p}}}
\newcommand\vq{{\Vector{q}}}
\newcommand\vr{{\Vector{r}}}
\newcommand\vs{{\Vector{s}}}
\newcommand\vt{{\Vector{t}}}
\newcommand\vu{{\Vector{u}}}
\newcommand\vv{{\Vector{v}}}
\newcommand\vw{{\Vector{w}}}
\newcommand\vx{{\Vector{x}}}
\newcommand\vy{{\Vector{y}}}
\newcommand\vz{{\Vector{z}}}

\newcommand\valpha{{\Vector{\alpha}}}
\newcommand\vbeta{{\Vector{\beta}}}
\newcommand\vgamma{{\Vector{\gamma}}}
\newcommand\vdelta{{\Vector{\delta}}}
\newcommand\vepsilon{{\Vector{\epsilon}}}
\newcommand\vtheta{{\Vector{\theta}}}
\newcommand\viota{{\Vector{\iota}}}
\newcommand\vkappa{{\Vector{\kappa}}}
\newcommand\vlambda{{\Vector{\lambda}}}
\newcommand\vmu{{\Vector{\mu}}}
\newcommand\vnu{{\Vector{\nu}}}
\newcommand\vxi{{\Vector{\xi}}}
\newcommand\vpi{{\Vector{\pi}}}
\newcommand\vrho{{\Vector{\rho}}}
\newcommand\vsigma{{\Vector{\sigma}}}
\newcommand\vtau{{\Vector{\tau}}}
\newcommand\vupsilon{{\Vector{\upsilon}}}
\newcommand\vphi{{\Vector{\phi}}}
\newcommand\vchi{{\Vector{\chi}}}
\newcommand\vpsi{{\Vector{\psi}}}
\newcommand\vomega{{\Vector{\omega}}}


% Matrix
\newcommand\MATRIX[1]{\symbf{#1}}

\newcommand\mA{{\MATRIX{A}}}
\newcommand\mB{{\MATRIX{B}}}
\newcommand\mC{{\MATRIX{C}}}
\newcommand\mD{{\MATRIX{D}}}
\newcommand\mE{{\MATRIX{E}}}
\newcommand\mF{{\MATRIX{F}}}
\newcommand\mG{{\MATRIX{G}}}
\newcommand\mH{{\MATRIX{H}}}
\newcommand\mI{{\MATRIX{I}}}
\newcommand\mJ{{\MATRIX{J}}}
\newcommand\mK{{\MATRIX{K}}}
\newcommand\mL{{\MATRIX{L}}}
\newcommand\mM{{\MATRIX{M}}}
\newcommand\mN{{\MATRIX{N}}}
\newcommand\mO{{\MATRIX{O}}}
\newcommand\mP{{\MATRIX{P}}}
\newcommand\mQ{{\MATRIX{Q}}}
\newcommand\mR{{\MATRIX{R}}}
\newcommand\mS{{\MATRIX{S}}}
\newcommand\mT{{\MATRIX{T}}}
\newcommand\mU{{\MATRIX{U}}}
\newcommand\mV{{\MATRIX{V}}}
\newcommand\mW{{\MATRIX{W}}}
\newcommand\mX{{\MATRIX{X}}}
\newcommand\mY{{\MATRIX{Y}}}
\newcommand\mZ{{\MATRIX{Z}}}

\newcommand\mGamma{{\MATRIX{\Gamma}}}
\newcommand\mDelta{{\MATRIX{\Delta}}}
\newcommand\mTheta{{\MATRIX{\Theta}}}
\newcommand\mLambda{{\MATRIX{\Lambda}}}
\newcommand\mXi{{\MATRIX{\Xi}}}
\newcommand\mPi{{\MATRIX{\Pi}}}
\newcommand\mSigma{{\MATRIX{\Sigma}}}
\newcommand\mUpsilon{{\MATRIX{\Upsilon}}}
\newcommand\mPhi{{\MATRIX{\Phi}}}
\newcommand\mPsi{{\MATRIX{\Psi}}}
\newcommand\mOmega{{\MATRIX{\Omega}}}


% Tensor
\newcommand\tens[1]{\symbfsf{#1}}
\newcommand\tA{{\tens{A}}}
\newcommand\tB{{\tens{B}}}
\newcommand\tC{{\tens{C}}}
\newcommand\tD{{\tens{D}}}
\newcommand\tE{{\tens{E}}}
\newcommand\tF{{\tens{F}}}
\newcommand\tG{{\tens{G}}}
\newcommand\tH{{\tens{H}}}
\newcommand\tI{{\tens{I}}}
\newcommand\tJ{{\tens{J}}}
\newcommand\tK{{\tens{K}}}
\newcommand\tL{{\tens{L}}}
\newcommand\tM{{\tens{M}}}
\newcommand\tN{{\tens{N}}}
\newcommand\tO{{\tens{O}}}
\newcommand\tP{{\tens{P}}}
\newcommand\tQ{{\tens{Q}}}
\newcommand\tR{{\tens{R}}}
\newcommand\tS{{\tens{S}}}
\newcommand\tT{{\tens{T}}}
\newcommand\tU{{\tens{U}}}
\newcommand\tV{{\tens{V}}}
\newcommand\tW{{\tens{W}}}
\newcommand\tX{{\tens{X}}}
\newcommand\tY{{\tens{Y}}}
\newcommand\tZ{{\tens{Z}}}


% Graph
\newcommand\gA{{\mathcal{A}}}
\newcommand\gB{{\mathcal{B}}}
\newcommand\gC{{\mathcal{C}}}
\newcommand\gD{{\mathcal{D}}}
\newcommand\gE{{\mathcal{E}}}
\newcommand\gF{{\mathcal{F}}}
\newcommand\gG{{\mathcal{G}}}
\newcommand\gH{{\mathcal{H}}}
\newcommand\gI{{\mathcal{I}}}
\newcommand\gJ{{\mathcal{J}}}
\newcommand\gK{{\mathcal{K}}}
\newcommand\gL{{\mathcal{L}}}
\newcommand\gM{{\mathcal{M}}}
\newcommand\gN{{\mathcal{N}}}
\newcommand\gO{{\mathcal{O}}}
\newcommand\gP{{\mathcal{P}}}
\newcommand\gQ{{\mathcal{Q}}}
\newcommand\gR{{\mathcal{R}}}
\newcommand\gS{{\mathcal{S}}}
\newcommand\gT{{\mathcal{T}}}
\newcommand\gU{{\mathcal{U}}}
\newcommand\gV{{\mathcal{V}}}
\newcommand\gW{{\mathcal{W}}}
\newcommand\gX{{\mathcal{X}}}
\newcommand\gY{{\mathcal{Y}}}
\newcommand\gZ{{\mathcal{Z}}}


% Sets
\newcommand\sA{{\mathbb{A}}}
\newcommand\sB{{\mathbb{B}}}
\newcommand\sC{{\mathbb{C}}}
\newcommand\sD{{\mathbb{D}}}
% Don't use a set called E, because this would be the same as our symbol
% for expectation.
\newcommand\sF{{\mathbb{F}}}
\newcommand\sG{{\mathbb{G}}}
\newcommand\sH{{\mathbb{H}}}
\newcommand\sI{{\mathbb{I}}}
\newcommand\sJ{{\mathbb{J}}}
\newcommand\sK{{\mathbb{K}}}
\newcommand\sL{{\mathbb{L}}}
\newcommand\sM{{\mathbb{M}}}
\newcommand\sN{{\mathbb{N}}}
\newcommand\sO{{\mathbb{O}}}
\newcommand\sP{{\mathbb{P}}}
\newcommand\sQ{{\mathbb{Q}}}
\newcommand\sR{{\mathbb{R}}}
\newcommand\sS{{\mathbb{S}}}
\newcommand\sT{{\mathbb{T}}}
\newcommand\sU{{\mathbb{U}}}
\newcommand\sV{{\mathbb{V}}}
\newcommand\sW{{\mathbb{W}}}
\newcommand\sX{{\mathbb{X}}}
\newcommand\sY{{\mathbb{Y}}}
\newcommand\sZ{{\mathbb{Z}}}


% Random variables
\newcommand\RandomVariable[1]{\symit{#1}}

\newcommand\rA{{\RandomVariable{A}}}
\newcommand\rB{{\RandomVariable{B}}}
\newcommand\rC{{\RandomVariable{C}}}
\newcommand\rD{{\RandomVariable{D}}}
\newcommand\rE{{\RandomVariable{E}}}
\newcommand\rF{{\RandomVariable{F}}}
\newcommand\rG{{\RandomVariable{G}}}
\newcommand\rH{{\RandomVariable{H}}}
\newcommand\rI{{\RandomVariable{I}}}
\newcommand\rJ{{\RandomVariable{J}}}
\newcommand\rK{{\RandomVariable{K}}}
\newcommand\rL{{\RandomVariable{L}}}
\newcommand\rM{{\RandomVariable{M}}}
\newcommand\rN{{\RandomVariable{N}}}
\newcommand\rO{{\RandomVariable{O}}}
\newcommand\rP{{\RandomVariable{P}}}
\newcommand\rQ{{\RandomVariable{Q}}}
\newcommand\rR{{\RandomVariable{R}}}
\newcommand\rS{{\RandomVariable{S}}}
\newcommand\rT{{\RandomVariable{T}}}
\newcommand\rU{{\RandomVariable{U}}}
\newcommand\rV{{\RandomVariable{V}}}
\newcommand\rW{{\RandomVariable{W}}}
\newcommand\rX{{\RandomVariable{X}}}
\newcommand\rY{{\RandomVariable{Y}}}
\newcommand\rZ{{\RandomVariable{Z}}}

% Random vectors
\newcommand\RandomVector[1]{\symbf{#1}}

\newcommand\rvA{{\RandomVector{A}}}
\newcommand\rvB{{\RandomVector{B}}}
\newcommand\rvC{{\RandomVector{C}}}
\newcommand\rvD{{\RandomVector{D}}}
\newcommand\rvE{{\RandomVector{E}}}
\newcommand\rvF{{\RandomVector{F}}}
\newcommand\rvG{{\RandomVector{G}}}
\newcommand\rvH{{\RandomVector{H}}}
\newcommand\rvI{{\RandomVector{I}}}
\newcommand\rvJ{{\RandomVector{J}}}
\newcommand\rvK{{\RandomVector{K}}}
\newcommand\rvL{{\RandomVector{L}}}
\newcommand\rvM{{\RandomVector{M}}}
\newcommand\rvN{{\RandomVector{N}}}
\newcommand\rvO{{\RandomVector{O}}}
\newcommand\rvP{{\RandomVector{P}}}
\newcommand\rvQ{{\RandomVector{Q}}}
\newcommand\rvR{{\RandomVector{R}}}
\newcommand\rvS{{\RandomVector{S}}}
\newcommand\rvT{{\RandomVector{T}}}
\newcommand\rvU{{\RandomVector{U}}}
\newcommand\rvV{{\RandomVector{V}}}
\newcommand\rvW{{\RandomVector{W}}}
\newcommand\rvX{{\RandomVector{X}}}
\newcommand\rvY{{\RandomVector{Y}}}
\newcommand\rvZ{{\RandomVector{Z}}}

\newcommand\laplace{\mathrm{Laplace}} % Laplace distribution

\newcommand\E{\mathbb{E}}
\newcommand\Ls{\mathcal{L}}
\newcommand\R{\mathbb{R}}
\newcommand\emp{\tilde{p}}
\newcommand\lr{\alpha}
\newcommand\reg{\lambda}
\newcommand\rect{\mathrm{rectifier}}
\newcommand\softmax{\mathrm{softmax}}
\newcommand\sigmoid{\sigma}
\newcommand\softplus{\zeta}
\newcommand\KL{D_{\mathrm{KL}}}
\newcommand\Var{\mathrm{Var}}
\newcommand\standarderror{\mathrm{SE}}
\newcommand\Cov{\mathrm{Cov}}
% Wolfram Mathworld says $L^2$ is for function spaces and $\ell^2$ is for vectors
% But then they seem to use $L^2$ for vectors throughout the site, and so does
% wikipedia.
\newcommand\normlzero{L^0}
\newcommand\normlone{L^1}
\newcommand\normltwo{L^2}
\newcommand\normlp{L^p}
\newcommand\normmax{L^\infty}

\DeclareMathOperator*{\argmax}{arg\,max}
\DeclareMathOperator*{\argmin}{arg\,min}

\DeclareMathOperator{\sign}{sign}
\DeclareMathOperator{\Tr}{Tr}
\let\ab\allowbreak
